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Lectures on Infinitary Model Theory (Lecture Notes in Logic #46) by David Marker at Abbey's Bookshop,
Lectures on Infinitary Model Theory (Lecture Notes in Logic #46)
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David Marker

Lectures on Infinitary Model Theory

Lecture Notes in Logic #46

David Marker

$214.95

Hardback

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English
Cambridge University Press
27 October 2016
Mathematical logic; Set theory; Algebraic geometry
Series: Lecture Notes in Logic
Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
By:  
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   46
Dimensions:   Height: 236mm,  Width: 160mm,  Spine: 18mm
Weight:   430g
ISBN:   9781107181939
ISBN 10:   1107181933
Series:   Lecture Notes in Logic
Pages:   192
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Introduction; Part I. Classical Results in Infinitary Model Theory: 1. Infinitary languages; 2. Back and forth; 3. The space of countable models; 4. The model existence theorem; 5. Hanf numbers and indiscernibles; Part II. Building Uncountable Models: 6. Elementary chains; 7. Vaught counterexamples; 8. Quasinimal excellence; Part III. Effective Considerations: 9. Effective descriptive set theory; 10. Hyperarithmetic sets; 11. Effective aspects of Lω1,ω; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.

David Marker is LAS Distinguished Professor of Mathematics at the University of Illinois, Chicago, and a Fellow of the American Mathematical Society. His main area of research is model theory and its connections to algebra, geometry and descriptive set theory. His book, Model Theory: An Introduction, is one of the most frequently used graduate texts in the subject and was awarded the Shoenfield Prize for expository writing by the Association for Symbolic Logic.

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